Nyquist Theorem
Equation expressing maximum data rate for a finite bandwidth noiseless channel |
If signal is run through a low-pass filter of bandwidth B |
The filtered signal can be completely reconstructed by making only 2B samples per second |
Sampling faster than 2B x per second is pointless |
Higher frequency components have already been filtered out. |
B = channel bandwidth
V = discrete levels the signal consists of
Max data rate = 2B log₂ V bits/sec
Twisted Pair
A form of transmission media |
Two insulated copper wires (1mm thick) |
Twisted in helical form (like DNA) |
Wires are twisted so the waves cancel out |
Used for transmitting analog or digital information |
Bandwidth depends on wire thickness and distance traveled |
Several megabits/sec for a few kilometers |
Widely used |
Adequate performance and cheaper |
UTP |
Unshielded Twisted Pair |
Cat 5 UTP cable, mostly in office buildings: |
4 pairs of twisted insulated wires in a single plastic sheath. |
Full-Duplex |
Links can be used in both directions at the same time, like a two-way road |
Half-Duplex |
Link can be used in either direction, only one way at a time |
Simplex |
Links that allow traffic in only one direction. |
Digital Modulation
Process of converting between bits and signals |
To send digital information, we must devise analog signals to represent bits |
Baseband Transmission
Signals occupies frequency from zero up to a maximum |
The maximum frequency depends on the signaling rate. |
Clock recovery
The process of extracting timing information from a data stream for the receiver to decode |
To encode bits into symbols, receiver must know when one symbol ends and the next begins |
Receiver needs to reference a clock of the same frequency |
Accurate clocks are expensive |
Another strategy must be used |
Overhead Definition
Overhead is any combination of excess or indirect computation time, memory, bandwidth, or other resources that are required to perform a specific task. |
NRZ
Non-return to zero |
Simplest, literal line code |
-V for 0 |
+V for 1 |
A long run of 0's or 1's leaves the signal unchanged |
Differentiating between bits become difficult. A long line of 15 0's looks like 16 without a very accurate clock |
Bandwidth Efficiency
For NRZ, it moves between + and - levels every 2 bits |
Requires bandwidth of at least B/2 when the bit rate is B bits/sec |
This limits the speed, as more bandwidth is required to run faster. |
Using more than two signalling levels, the limited bandwidth can be used for efficiently |
e.g. using 4 voltages, 2 bits can be sent at once, as a single symbol |
Effective only if the receiver can distinguish the 4 levels |
The signal change rate is now half the bit rate, thus reducing the required bandwidth. |
The rate the signal changes is the symbol rate |
the bit rate is the symbol rate multiplied by the number of bits per symbol |
NRZI
The inverted vesion of NRZ |
transition for 1 |
no transition for 0 |
Used by USB |
Universal Serial Bus |
Manchester
Used for classic Ethernet |
low to high = 0 |
high to low = 1 |
Requires twice as much bandwidth as NRZ because of the clock |
Adds 100% overhead |
Guarantees clock recovery and balanced signal because: |
-Each bit is modulated in a balanced signal |
Bipolar Encoding (AKA Alternate Mark Inversion)
0 = logical zero |
Encodes 0's with a zero-signal |
1 = + or - |
Encodes 1 with positive or negative level |
In telephone networks, it is know as Alternate Mark Inversion(AMI), where "mark" is 1 and "space" is 0. |
Guarantees a balanced signal because: |
-1's are encoded in alternating +V, - V signal levels |
If -V is a logical zero, and the two voltages +1V and -1V represents a logical zero, to send "1", the transmitter alternates between +1V and -1V.
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Balanced Signal
Base-band signal averages zero |
As much + voltage as -, even after short period of time |
No DC electrical components |
Advantangeous, as some channels (coaxial or lines with transformers) attenuate a DC component due to their physical properties |
DC component filtered out |
Avoids energy waste |
Provides better clock recovery |
Through transitions, due to mix of + and - volatages. |
Allows measuring the signal average |
For error detection and receiver calibration. Impossible with an unbalanced signal |
Link Failure
Instances for possible link failure: |
Sequence used for scrambling could be the same as the signal |
Transmitting all 0's, constituting a link failure |
With unbalanced signals, the average may drift from the true decision level due to a density of 1s, for example, which would cause more symbols to be decoded with errors.
Capacity Coupling
Method of connecting the reciever to the channel. |
Passes only the AC portion of the signal. |
4B/5B
A form of line code |
Maps groups of 4 bits of data onto groups of 5 bits for transmission |
Used to prevent more than 3 consecutive 0's |
Every data (4B) has a fixed codeword(5) that it is translated to |
This scheme adds 25% overhead |
Better than the 100% overhead of Manchester encoding |
Non-data codes can represent physical layer control signals |
e.g: "11111" - idle line |
"11000" = start of a frame |
Produces at least two transitions per 5 bits of output code, regardless of input data. |
8B/10B
Maps 8 bits input onto 10 bits output |
80% efficient |
Achieves DC signal balance, never far from balanced |
At most 2 bit disparity |
8 bits of data are transmitted as a 10-bit entity called a symbol |
Low 5 bits are encoded into a 6 bit group |
5b/6b portion |
Top 3 bits encoded into a 4-bit group |
3b/4b portion |
These groups are concatenated together to form a 10-bit symbol that is transmitted. |
Standards also define up to 12 symbols that can be sent in place of a data symbol |
These indicate start-of-frame, end-of-frame, link idle, etc. |
Helps clock recovery, never more than 5 consecuive 1s or 0s |
Passband Transmission
Signals that are shifted to occupy a higher range of frequencies, (all wireless transmissions) |
Scheme that regulates the amplitude, phase or frequency of a carrier signal to convey bits. |
Occupies a band of frequencies around the frequency of the carrier signal. |
Common for wireless and optical channels. |
Regulatory constraints and intereference prevention dictates choice of frequencies. |
Modulating the amplitude, frequency/phase of a carrier signal sends bits in a (non-zero) frequency range |
Passband Transmission Image
Regulating/modulating a carrier
Amplitude Shift Keying (ASK) |
-Two different amplitudes represent 0 and 1 |
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-More levels can represent more sumbols |
Frequency Shift Keying (FSK) |
-Two or more tones used |
Phase Shift Keying(PSK) |
- Carrier wave systematicaly shifted 0 or 180 dgrees at each symbol period. |
Schemes can be combined and more levels used to transmit more bits per symbol. However, only one of frequency and phase can be modulated as they are related.
Frequency Shift Keying (FSK)
Two frequencies used |
one symbol for 0, another for 1 |
Phase Shift Keying - PSK
Only Phase is modulated through time |
to identify points on the plane |
Amplitude stays constant, not modulated |
Each point corresponds to one of four symbols. |
2 bits per symbol transmitted |
Example:
To indentify 4 vertices("quadrature") of a square centered plane. Each point corresponds to 4 symbols.
As there are 4 symbols, 2 bits per symbol are transmitted.
Constellation Diagrams
Shorthand to capture the amplitude and phase modulations symbols |
The points give the legal amplitude and phase combinations of each symbol. |
The phase of a dot is indicated by the angle a line from it to the origin makes with the positive x-axis |
The amplitude of a dot is the distance from the origin |
Constellation Diagram Image
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QAM-16
QAM |
Quadrature Amplitude Modulation |
16 combinations of amplitudes and phase used |
Can transmit 4 bits per symbol |
A denser modulation scheme with 64 different combinations is called QAM-64. There are even higher-order QAMs used.
Gray-Coding
Assigns(maps) bits to symbols so that adjacent symbols differ in only 1 bit position |
If a receiver decodes the symbol in error |
It will make only a single bit in error |
Gray-coding Image
Gray-coded QAM-16 constellation
Multiplexing
Channels shared by multiple signals |
More convenient than using a single wire to carry several signals than to install a wire for every signal. |
Frequency Division Multiplexing(FDM)
Divides the spectrum into frequency bands. e.g. AM radio |
Shares the channel by placing users on different frequencies |
Frequencies are allocated different logical channels, with interchannel separation great enough to prevent interference |
Subcarriers are coordinated to be tightly packed |
Filters limit the useable bandwidth to 3100hz p/voice-grade channel. |
Many channels multiplexed together, 4000hz allocated per channel |
Different frequencies encode different values, while phase and amplitude remain constant. |
Higher frequency is associated to 1 bit, and a lower to 0 |
Separations(the excess) are called guard bands. Even though there is a large gap, some adjacent channels do overlap because filters do not have ideal 'sharp edges', therefore a strong spike at the edge of one channel will be felt in jacanet as nonthermal noise
Frequency Division Multiplexing Image
(a) The original bandwidths
(b) The bandwidths raised in frequency
(c) The Multiplexed channel
Orthogonal FDM (OFDM)
OFDM (Orthogonal FDM) is an efficient FDM technique used for 802.11, 4G cellular and other communications that does not use guard bands. |
The channel is divided into many subcarriers that independently send data. |
Subcarriers are tightly packed in the frequency domain. |
Frequency response of each subcarrieris zero at the center of adjacent subcarriers, therefore subcarriersbe sampled at their center frequencies without interference from neighbours |
Guard time required to repeat ports of symbol signals so that they have the desired frequency |
Time Division Multiplexing
Shares a channel over time |
Users take turns on a fixed schedule |
Not packet switching |
Each gets the entire badwidth for a little burst of time |
Bits from each input stream are taken in a fixed time slot and output to the aggregate stream. |
This stream runs the sum rate of individual streams. |
Streams must be synchronized in time. |
Widely used in telephone/cellular systems |
Small intervals of guard time analoguous to a requency guard band may be added to accomodate small timing variations
Time Division Multiplexing Image
Three streams being multiplexed with TDM.
Code Divison Multiple Access
Shares the channel by giving users a code |
Codes are orthogonal |
Can be sent at the same time |
Widely used as part of 3G networks |
Scalar Product (example): |
A ● B = (a₁, a₂, a₃) ● (b₁, b₂, b₃) = a₁b₁ + a₂b₂ + a₃b₃ |
Walsh Codes (example):
A = (a₁ , a₂, a₃) A̅ = (-a₁ , -a₂, -a₃)
B =(b₁ , b₂, b₃) B̅ = (-b₁ , -b₂, -b₃)
Properties of CDMA codes:
For all A, B with A ≠ B
A ● A = +1
A ● A̅ = -1
A ● B = A B = 0
Transmission:
A, B and C transmit 1, 1 and 0 respectively
A, B and C send codes A, B and C̅ respectively
The receiver sees A + B + C̅
Code Division Multiple Access(CDMA)
A form of spread spectrum communication |
Narrowband signal spread out over a wider frequency band |
Tolerant of interference. |
Allows multiple signals from different users to share the same frequency band. |
CDMA shares the channel by giving users a code |
Codes are orthogonal; |
Can be sent at the same time |
Widely used as part of 3G networks |
Each station can transmit over the entire frequency spectrum all the time |
Can also be called "Code Division Multiplexing", but because it is used mostly to allow the same frequency band to be shared by different users by multiple signals, it was commonly called Code Division Multiple Access
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